Technical Field
Embodiments of the subject matter disclosed herein generally relate to seismic data processing, more particularly, to obtaining an enhanced image of structures under complex geological regions with strong velocity contrast and substantial attenuation, by compensating for visco-acoustic effects in a tilted transverse isotropy (TTI) medium while applying a reverse time migration (RTM) method.
Discussion of the Background
In spite of the momentary over-supply of fossil fuel, interest in developing new oil and gas production fields remains strong for both land and offshore locations. Drilling is an expensive process. Therefore, before engaging in such a costly undertaking, geophysical surveys are performed to achieve more accurate information about underground formations (the term “underground” includes under the seafloor). Data acquired during geological surveys is processed to generate a profile (image) of the underground formations. While this profile does not provide an accurate location of oil and gas, it suggests, to those trained in the field, the presence or absence of oil and/or gas.
FIG. 1 illustrates a marine seismic survey during which seismic data is collected to explore a geological structure under the seafloor. Vessel 10 tows an array of seismic receivers 12 provided on cables 14 that form streamers 16 (only one is visible in this vertical view, but plural streamers may be arranged in a horizontal xy plane), at a depth z1 below water surface 18. The streamers may be towed horizontally (at substantially constant depth z1 throughout their length during the survey as illustrated), arranged in a slanted or curved configuration (i.e., depth varying along the streamer), or at different depths. Vessel 10 may also tow a wave source 20 configured to generate waves 22a. Waves 22a propagate down toward the seafloor 24 penetrate it and are then partially reflected and/or refracted at interfaces between layers where the wave propagation velocity changes. Reflected acoustic waves such as 22b and 22c (redirected upward by reflector 26) may be detected by receivers 12 directly as emerging from the seafloor and/or as ghost reflections from the water surface, such as 22d. Data (wave amplitude versus time series) recorded by the receivers is processed to extract information about the underground formations. Processing may include various phases, e.g., velocity model determination, pre-stack migration, post-stack processing, etc., which are known in the art.
It has been observed (as discussed in the book, Quantitative Seismology, by Aki and Richards, published 1980 by W.H. Freeman & Co, relevant portions of which are incorporated by reference) that the anelastic effects (e.g., anelastic attenuation, which is characterized by seismic quality factor Q that is inversely proportional to attenuation) cause seismic energy to decrease along the path and wavelet distortion. For example, gas trapped in overburden (i.e., above structures of interest such as an oil reservoir) can strongly attenuate seismic P-waves. As a result, not only is the migrated amplitude dim below the gas, but the imaging resolution is also greatly reduced due to high-frequency energy loss and phase distortion.
Some conventional methods (as described, e.g., in Kjartansson,'s 1979 article, “Constant Q-wave propagation and attenuation,” in the Journal of Geophysical Research 84, B9, pages 4,737-4,748; Bickel et al.'s 1985 article, “Plane-wave Q deconvolution,” published in Geophysics 50, pages 1,426-1,439; and/or Calvert et al.'s 1991 article, “Inverse Q-filtering by Fourier transform,” in Geophysics 56, pages 519-527, the contents of which are incorporated herein in their entirety) compensate for the seismic absorption in the data domain using an inverse Q-filter. These methods are based on one-dimensional backward propagation and cannot correctly handle real geological complexity. Some methods correct for anelastic attenuation and dispersion in a pre-stack depth migration (a logical choice since these phenomena occur during wave propagation). However, most migration methods usually treat the underground formation's model as a lossless acoustic medium, attempting to correct only for the amplitude effect due to geometric spreading (see, e.g., relevant portions of the book, Mathematics of multidimensional seismic inversion, by Bleistein et al., Springer Publishing Company, 2001). Two main reasons account for this situation. First, it is difficult to accurately estimate the Q factor from seismic data. Second, the technology of migrating seismic data using a visco-acoustic equation or an anelastic equation has not been well-established.
In a generalized method for estimating absorption losses (e.g., as described in Xin et al.'s 2008 article, “3D tomographic amplitude inversion for compensating amplitude attenuation in the overburden,” in 78th SEG Annual International Meeting, Expanded Abstracts, pages 3,239-3,243, the content of which is incorporated herein in its entirety), the analysis is performed on the migrated data and based on a tomographic velocity updating algorithm (e.g., as described by Zhou et al.'s 2003 article, “Tomographic residual curvature analysis: The process and its components,” in 73 SEG Annual International Meeting, Expanded Abstracts, pages 666-669, the content of which is incorporated herein in its entirety). Efficient approaches for compensation of frequency-dependent dissipation effects in Kirchhoff and Gaussian beam pre-stack depth migration making use of the absorption model estimated from a 3D tomographic amplitude inversion apply Q compensation during migration, fully honor actual raypaths (see, e.g., Xie et al.'s 2009 article, “3D prestack depth migration with compensation for frequency-dependent absorption and dispersion,” in 79th SEG Annual International Meeting, Expanded Abstracts, pages 2,919-2,922; and Xie et al.'s 2010 article, “3D prestack beam migration with compensation for frequency dependent absorption and dispersion,” presented at the 72nd EAGE Annual International Conference and Exhibition, the contents of which are incorporated herein in their entirety).
Some effort has been made to develop an inverse Q-migration using one-way wave equation migration (see, e.g., Dai et al. 1994's article, “Inverse Q-migration,” in 64th SEG Annual International Meeting, Expanded Abstracts, pages 1,418-1,421; and Yu et al.'s 2002 article, “Compensation for the effects of shallow gas attenuation with visco-acoustic wave-equation migration,” in 72nd SEG Annual International Meeting, Expanded Abstracts, pages 2,062-2,065, the contents of which are incorporated herein in their entirety). The one-way wave equation is in this case formulated in the frequency domain to directly account for frequency-dependent dissipation. RTM based on directly solving the two-way wave equation provides a superior way to image complex geologic regions and has become a standard migration tool for subsalt imaging, especially in the Gulf of Mexico. A time domain wave equation to model the visco-acoustic effects is needed to incorporate an attenuation correction in RTM. A pseudo-differential equation to model isotropic visco-acoustic waves based on the dispersion relation has been applied in reverse time migration to compensate for the anelastic effects in seismic images (see, e.g., Zhang et al.'s 2010 article, “Compensating for visco-acoustic effects in reverse-time migration,” 80th SEG Annual International Meeting, Expanded Abstracts, pages 3,160-3,164, the content of which is incorporated herein in its entirety). However, extending Zhang's approach to formulate visco-acoustic TTI RTM is difficult, if at all possible.
Alternatively, a visco-elastic mechanical model consisting of standard linear solids (SLSs) has been proposed to model real earth materials and employed to solve the visco-elastic wave equation for forward modeling (see, e.g., Robertsson et al.'s 1994 article, “Viscoelastic finite-difference modeling,” in Geophysics 59, pages 1,444-1,456, the content of which is incorporated herein in its entirety). In this approach, one SLS consists of a spring in parallel with a spring and a dashpot in series, and can approximate a constant Q within a defined frequency band with a series of SLSs connected in parallel (as described in Day et al.'s 1984 article, “Numerical simulation of attenuated wavefields using Pade approximation method,” in the Geophysical Journal of Royal Astronomy Society 78, pages 105-118, the content of which is incorporated herein in its entirety). In an SLS, the stress-strain relationship is expressed as a causal time convolution of a stress relaxation function with the strain rate. This time dependence of the relaxation mechanism is governed by stress and strain relaxation times. A visco-elastic rheology with multiple relaxation mechanisms can explain experimental observations of wave propagations in the earth. Carcione et al. (1988) designed a system of equations of motion and introduced memory variables to obviate storing the entire strain history required by the time convolution. This visco-acoustic wave propagation based on multiple relaxation mechanisms can be extended to account for anisotropy; however, the time reversal propagation is unstable, which poses challenges in implementing visco-acoustic TTI RTM.
It is desirable to develop RTM methods that compensate for the absorption effects in TTI medium to obtain enhanced images of structures under complex geological regions with strong velocity contrast and substantial attenuation.